| Blind source separation（BSS） is the technique which can separate out original signals from some observed mixed signals according to certain conditions and assumptions without knowing any priori information on the source signals. In the past few decades, the techniques of blind signal separation have gained more and more attentions from many scholars, and have obtained extremely rapid development because of its numerous potential applications.In practice, signals such as communication signals, voice signals, medical signals and underwater acoustic signals are inevitably affected by noise of various forms. Most of the BSS algorithms have the best performance in the absence of noise, and their effectiveness is definitely decreased in the presence of additive noise. It may even lead to separation failure when the signals are seriously corrupted by noise. Unable to get more priori information about the source signal and without knowing the channel parameters make the noisy BSS problem more complex than the ideal BSS model. However, at present, researches on the noisy BSS are relatively insufficient.This paper studies the noisy blind source separation, especially the noisy BSS algorithms based on bias removal and the noisy BSS algorithms based on denoising. Then, the proposed noisy BSS algorithms are applied to underwater acoustic signals, and the experimental simulation shows that the proposed algorithms are applicable and effective in separating noisy underwater acoustic signals.The main work in this paper is summarized as follows:1. This paper studies the estimation algorithm of the number of the source signals in BSS. Since the performance of the existing source number estimation algorithms are not robust in low SNR, we proposes a turning point detection algorithm based on singular value decomposition, and the experimental results show that this algorithm can improve the estimation performance in low SNR. The performance of the two BSS algorithms, namely, —Fast ICA and Robust ICA—, is analyzed and compared in detail. Simulation experiments are carried out for sub-Gaussian sources, super-Gaussian sources, and mixed sources of sub-Gaussian and super-Gaussian sources at different SNR level and at different sampling points. The results show that the overall performance of the Robust ICA algorithm is more robust.2. This paper also studies the noisy BSS algorithms based on bias removal. For overdetermined BSS model we propose a quasi-whitened Fast ICA algorithm based on eigenvalue decomposition. This algorithm can estimate the noise variance through eigenvalue decomposition so as to whiten the useful signals in the mixtures and remove the deviation introduced by the noise, while reducing the dimension of the signal space which can translate overdetermined model into determined model. Moreover, for the channel mixtures whose SNR levels are not exactly the same, we propose a twice whitened Fast ICA algorithm based on iteration. The algorithm can accurately estimate the noise variance of each channel mixture, and thus more accurately remove bias introduced by the noise, which makes the whitening of the useful signals more effective. Simulation results prove that these two algorithms are effective in solving the noisy BSS problem.3. This paper studies the strategy which combines the denoising algorithm and the BSS algorithm. Currently there are denoising preprocessing, denoising post-processing and the cascade of denoising preprocessing and post-processing. This paper focuses on the in-depth study of denoising preprocessing algorithm and discusses the solving strategies of the cascade of denoising preprocessing and post-processing. Since the serial and parallel modes proposed in the literature do not make full use of the information available such as the separation matrix and the estimation signals, in this paper we propose an improved parallel cascade mode which can utilize the two channel outputs. The simulation experiments show that this method has better performance than the existing serial and parallel modes.4. Besides, as a denoising preprocess, wavelet denoising algorithm is studied in-depth. Considering the poor performance of the wavelet denoising algorithm in low SNR, we propose an improved wavelet denoising algorithm based on translation invariant. The algorithm optimizes the key parameters of the wavelet denoising algorithm, presents a more robust noise variance estimation algorithm, i.e., high frequency coefficient sliding window algorithm, and then narrows the range of translation invariant, which can reduce the computation amount without reduce the denoising effect. Then, we apply the denoising algorithm to noisy BSS problem and the simulation results verify the effectiveness of the algorithm. For the denoising of Gaussian colored noise, we propose a wavelet denoising algorithm using the improved layering GCV threshold estimation algorithm. This algorithm is applied to the BSS with Gaussian colored noise, and the simulation results show that the algorithm can remove Gaussian colored noise more effectively and enhance the performance of the BSS algorithm.5. Moreover, as a denoising preprocessing algorithm, denoising algorithm based on Empirical Mode Decomposition（EMD） is also studied. Since the traditional empirical mode decomposition denoising algorithms have some weakpoints such as incomplete denoising and the possibility of removing the useful information as noise, a new piecewise EMD threshold denoising algorithm is proposed. This algorithm uses the mean period method to divide the IMFs into the noise-dominated part and the signal-dominated part, and then uses the traditional threshold algorithm to estimate the threshold of the noise-dominated IMFs, and uses an improved threshold algorithm which can decrease faster for the signal-dominated IMFs. At last, an improved thresholding technique is used to reconstruct the signal. The proposed algorithm can overcome the shortcomings of the existing algorithms and achieve better denoising performance. The algorithm is applied to noisy BSS, which can significantly improve the performance of BSS algorithm.This paper also studies the Gaussian colored noise denoising algorithm based on EMD. Research shows that the amplitude of the first IMF got by decomposing the Gaussian colored noise using EMD is smaller than the one of Gaussian white noise, and the amplitude of the other IMFs decreases very slowly. According to the characteristics of the Gaussian colored noise, the algorithm can adjust the parameters of the EMD threshold algorithm, and then use a piecewise threshold estimation algorithm. This algorithm is applied to the BSS problem containing Gaussian colored noise, and the experimental results demonstrate the effectiveness of the algorithm.6. The proposed noisy BSS algorithm is then applied in underwater acoustic signal processing. Since computer simulation signal has a special advantage in scientific research, we carry out simulation experiments for marine environment noise, acoustic test signals, underwater acoustic communication signals and ship radiated noise, and then for the determined model and the overdetermined model of BSS respectively.For the determined model, we mainly use two denoising algorithms for Gaussian colored noise as denoising preprocessing, namely, the improved layering GCV threshold wavelet denoising algorithm and the piecewise EMD threshold denoising algorithm, and then we use Robust ICA to separate. Simulation results show that the two algorithms can effectively remove the ocean ambient noise in underwater acoustic signals, and significantly improve the performance of BSS algorithm. We also discuss the relationship between the algorithm performance and the sampling rate. The experiments prove that increasing the sampling rate helps improve the performance of the denoising algorithm, and further enhances the performance of BSS algorithms.For the overdetermined model, we mainly use two noisy BSS algorithms based on bias removal, namely, quasi-whitened Fast ICA algorithm based on eigenvalue decomposition and twice whitened Fast ICA algorithm based on iteration. Simulation results show that for underwater acoustic communication signals, using Fast ICA, the signal mean square error（SMSE） is decreased to 10-2 order of magnitude when SNR >32d B, but using the proposed algorithm, it is so when SNR >14d B; for ship radiated noise, using Fast ICA, the SMSE is decreased to10-2 order of magnitude when SNR >22d B, but using the proposed algorithm, it is so when SNR >10d B. Therefore, the proposed algorithms can obtain a satisfactory separation. It is also verified that increasing the sampling rate almost has no effect on the performance of the BSS algorithm based on bias removal, so these algorithms are more robust. Therefore, noisy BSS algorithms based on bias removal is very effective in noisy underwater acoustic signal processing.
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